The demand for permanent magnet resolvers is rising significantly with the increase of operation speed in the electric propulsion system. In this paper, the rotor-pole number (RPN) cooperation strategy is proposed from the perspective of phase shift on the modular flux switching permanent magnet (FSPM) resolver with yokeless stator. The RPN cooperation strategy is deduced analytically by adjusting the angle fitting ratio under the fixed 90-degree sine and cosine winding phase shift electric angle. Moreover, its restrictions are also derived by the flux leakage and permeance analysis in certain cases. Therefore, the proposed cooperation strategy and its limitations enrich the field modulation principle in the PM resolver application. Based on the proposed cooperation strategy and its limitation, a series of proper rotor and stator combinations are proposed in the FSPM resolver with no more than 1.5% total harmonic distortion (THD) evaluated in finite element analysis (FEA).